Rule: Q[2, 4, 15, 44]

Type

This rule is of Legendre type.

Polynomials

One starts from the polynomial P1 and extends one by one with Pi until the final polynomial defining this rule is reached.
Note: Polynomials might be truncated due to size! The complete polynomials are included in the download.

Node locations in the complex plane

Plot of the node locations in the complex plane.

Magnitude of the Weights

Logarithmic magnitude of the weights
         plotted against the (real part) of the nodes.

Quadrature Rule Data

Nodes

Node (ball center) Error (ball radius)
0.99301799775063452644 - 5.3154308322434881126e-888j 6e-232, 6e-232j
-0.98576497525752196716 - 6.0051332803573214896e-892j 5.76e-232, 5.76e-232j
-0.91248695683407599658 + 2.5180348245576402263e-912j 6.93e-233, 6.93e-233j
-0.99972582526765616345 + 3.0317027931609624352e-922j 2.21e-232, 2.21e-232j
0.93173976074720094728 - 2.2700424271729631987e-941j 1.39e-232, 1.39e-232j
0.94882707947373850329 - 8.862371804484864419e-942j 2.34e-232, 2.34e-232j
0.96359754453680886232 - 2.7883701313320042194e-942j 3.61e-232, 3.61e-232j
-0.89127078387572171269 - 5.9066554628373438702e-950j 3.86e-233, 3.86e-233j
-0.99301799775063452644 + 6.1669994654526441278e-961j 6.29e-232, 6.29e-232j
0.99972582526765616345 - 3.8146328969183802825e-970j 2.19e-232, 2.19e-232j
0.86835858866418943113 - 4.5149353360266514063e-977j 1.87e-233, 1.87e-233j
0.9759380959115356208 - 5.1946951435945668421e-974j 4.76e-232, 4.76e-232j
-0.93173976074720094728 + 2.1063741175139490999e-976j 1.37e-232, 1.37e-232j
-0.84409246104555248852 - 3.4744617757401088709e-979j 8.11e-234, 8.11e-234j
0.98576497525752196716 - 3.2376329087101150943e-977j 5.7e-232, 5.7e-232j
0.76691029519065407282 + 2.4637531043553760636e-982j 3.79e-235, 3.79e-235j
0.91248695683407599658 - 7.9717625280408065835e-979j 7.46e-233, 7.46e-233j
-0.99765982878586334329 - 5.9197938085194413434e-976j 5.39e-232, 5.39e-232j
-0.76691029519065407282 - 1.7747926843725473508e-990j 3.95e-235, 3.95e-235j
-0.94882707947373850329 - 1.5488329594499755782e-984j 2.27e-232, 2.27e-232j
0.89127078387572171269 - 1.1881800040173457567e-988j 3.87e-233, 3.87e-233j
0.74015427484364559629 + 3.8396114105202749397e-993j 1.12e-235, 1.12e-235j
-0.86835858866418943113 + 1.33198635437761018e-987j 1.74e-233, 1.74e-233j
-0.81887367649914030941 + 4.1228306015853310376e-989j 3.28e-234, 3.28e-234j
-0.74015427484364559629 - 2.3608754645014817328e-992j 1.11e-235, 1.11e-235j
0.99765982878586334329 - 2.5134928454408403372e-987j 5.26e-232, 5.26e-232j
0.71222402572287055499 - 4.5278492152219273119e-993j 2.4e-236, 2.4e-236j
0.61505413906629502582 + 4.1969427975114874053e-996j 5.88e-239, 5.88e-239j
0.84409246104555248852 + 1.0500433824925922731e-991j 8.14e-234, 8.14e-234j
-0.65008297809674525171 + 6.6133099489512288467e-994j 5.61e-238, 5.61e-238j
-0.9759380959115356208 - 5.4012375568050104543e-987j 5.11e-232, 5.11e-232j
0.79308358720639064409 - 2.1860070397456259128e-999j 1.27e-234, 1.27e-234j
0.68238998000535864119 - 3.1310245785509127213e-1002j 4.38e-237, 4.38e-237j
-0.96359754453680886232 - 1.1487200683924756821e-999j 3.53e-232, 3.53e-232j
-0.71222402572287055499 - 7.4204974555469600363e-1008j 2.42e-236, 2.42e-236j
-0.68238998000535864119 + 2.1856282599296985168e-1009j 4.22e-237, 4.22e-237j
0.25859609927587487351 - 5.2316754014187255864e-1022j 8e-249, 8e-249j
0.57735026918962576451 + 8.937710063355937378e-1012j 5.21e-240, 5.21e-240j
0.81887367649914030941 + 1.3841865640273187634e-1008j 3.32e-234, 3.32e-234j
-0.61505413906629502582 - 6.1345621328945362204e-1012j 5.89e-239, 5.89e-239j
-0.57735026918962576451 + 6.4561053847037703698e-1014j 5.1e-240, 5.1e-240j
-0.79308358720639064409 - 1.5335232712553354028e-1015j 1.19e-234, 1.19e-234j
0.65008297809674525171 + 1.6416675058864498764e-1023j 6.01e-238, 6.01e-238j
0.53718464097059375059 - 4.6240989786436523374e-1029j 3.9e-241, 3.9e-241j
-0.1046627939667392394 + 9.2501372181719167169e-1041j 5.45e-253, 5.45e-253j
-0.49482362208327486907 - 1.9456164841757331746e-1028j 2.36e-242, 2.36e-242j
-0.53718464097059375059 - 1.4036545179862870663e-1031j 3.62e-241, 3.62e-241j
0.052418537473807716659 - 1.0765985731311857706e-1045j 2.19e-254, 2.19e-254j
0.49482362208327486907 - 4.3357975052751936315e-1032j 2.35e-242, 2.35e-242j
0.2079283588539873853 + 1.3936420578496361619e-1041j 3.13e-250, 3.13e-250j
-0.2079283588539873853 - 1.5094572041331759847e-1040j 3.82e-250, 3.82e-250j
-0.45053020586639054159 + 1.0680274681261135161e-1033j 1.47e-243, 1.47e-243j
-0.15655801081562154215 - 2.8921583652866737867e-1042j 1.3e-251, 1.3e-251j
0.45053020586639054159 + 3.2889122297038663547e-1033j 1.5e-243, 1.5e-243j
0.3570951438153437561 + 1.1971517986465252355e-1036j 4.41e-246, 4.41e-246j
-1.506064399770877393e-1072 + 2.3262532772047155385e-1072j 1.8e-1070, 1.8e-1070j
-0.40454684830174076377 + 1.7137193166322463028e-1034j 8.26e-245, 8.26e-245j
-0.25859609927587487351 - 3.1626088649512221741e-1039j 8.82e-249, 8.82e-249j
0.15655801081562154215 - 2.3888875244108497881e-1042j 1.24e-251, 1.24e-251j
0.40454684830174076377 - 6.4405625292209819971e-1036j 8.53e-245, 8.53e-245j
0.1046627939667392394 + 6.0610948551141149953e-1044j 6.26e-253, 6.26e-253j
-0.30838033490300779027 + 1.2870693643843334365e-1037j 2.01e-247, 2.01e-247j
-0.3570951438153437561 - 9.8119575171183534955e-1038j 4.26e-246, 4.26e-246j
-0.052418537473807716659 - 8.0975395681253231007e-1047j 2.47e-254, 2.47e-254j
0.30838033490300779027 - 7.6832055691463003531e-1038j 1.97e-247, 1.97e-247j

Weights

Weight (ball center) Error (ball radius)
0.0059514067383502250037 + 4.310797382928314832e-889j 3.69e-31, 1.22e-141j
0.0085481916064435603938 - 2.10207015863923832e-890j 1.65e-31, 5.45e-142j
0.020273128174050828557 + 8.2878380815839197601e-890j 7.73e-32, 2.55e-142j
0.0008916974663030651317 + 4.0623150341396238294e-891j 8.69e-32, 2.87e-142j
0.018199048607480837862 - 1.895177205593410261e-888j 1.62e-32, 5.34e-143j
0.015950569954961225748 + 1.9872379290790972034e-888j 1.4e-32, 4.62e-143j
0.013571665810653097001 - 2.3037662111634417869e-888j 5.78e-33, 1.91e-143j
0.022114862436532882245 - 1.165088483672233477e-889j 2.88e-34, 9.51e-145j
0.0059514067383502250037 + 1.5388541408673492385e-890j 1.98e-33, 6.55e-144j
0.0008916974663030651317 - 1.2285249197396013082e-888j 2.97e-34, 9.82e-145j
0.023652350714329873661 + 2.5002256243565150443e-888j 1.5e-35, 4.96e-146j
0.01109557331228209153 + 3.1032782327678579849e-888j 7.89e-34, 2.6e-144j
0.018199048607480837862 - 6.0602297243521938612e-890j 4.65e-36, 1.53e-146j
0.02481182176746894143 - 2.4477847894812195641e-889j 3.58e-37, 1.18e-147j
0.0085481916064435603938 - 5.7183603121951660171e-888j 5.14e-34, 1.7e-144j
0.026393715720001856432 + 4.7874277467466969688e-888j 2.12e-38, 7.01e-149j
0.020273128174050828557 + 1.9547661481384750732e-888j 1.51e-35, 4.99e-146j
0.0033324866593444542422 - 1.0683851615107069089e-890j 8.38e-37, 2.77e-147j
0.026393715720001856432 + 6.1566960352454182919e-889j 2.38e-40, 7.87e-151j
0.015950569954961225748 + 4.5518053458020042476e-890j 4.51e-38, 1.49e-148j
0.022114862436532882245 - 2.1523665411844755269e-888j 1.36e-37, 4.49e-148j
0.027221910462744362567 - 4.6609983303718961597e-888j 7.3e-41, 2.41e-151j
0.023652350714329873661 + 1.6777133260529470402e-889j 1.38e-38, 4.54e-149j
0.025559179714916674775 + 3.5381710468264101222e-889j 8.77e-40, 2.9e-150j
0.027221910462744362567 - 6.8060479450832192451e-889j 1.73e-41, 5.71e-152j
0.0033324866593444542422 + 4.678746319774310905e-888j 8.97e-38, 2.96e-148j
0.028765560614426159648 + 3.9392538468142356669e-888j 1.31e-42, 4.34e-153j
0.036392716599641311742 - 1.2477258543248268473e-888j 8.95e-45, 2.96e-155j
0.02481182176746894143 - 3.0147218484409151671e-888j 1.12e-40, 3.69e-151j
0.033654649912376344971 + 4.0908903135175403444e-889j 9.7e-46, 3.2e-156j
0.01109557331228209153 + 2.7587230552905908367e-890j 2.24e-41, 7.4e-152j
0.025985756081211679695 - 4.3594893480850486012e-888j 4.75e-43, 1.57e-153j
0.031000189626342100971 - 2.9171111324214767992e-888j 2.82e-45, 9.32e-156j
0.013571665810653097001 - 3.5018708239548459207e-890j 1.8e-41, 5.95e-152j
0.028765560614426159648 + 6.4914510728231790898e-889j 2.83e-45, 9.35e-156j
0.031000189626342100971 - 5.4120245346782618009e-889j 4.62e-46, 1.53e-156j
0.050256481507149051225 - 7.1851368287632133993e-890j 9.45e-52, 3.12e-162j
0.038977517724182456122 + 7.8472306236131325106e-889j 4.73e-48, 1.56e-158j
0.025559179714916674775 + 3.6764084036640378262e-888j 2.52e-43, 8.33e-154j
0.036392716599641311742 - 2.9341636448012883616e-889j 1.29e-48, 4.26e-159j
0.038977517724182456122 + 2.0780382997340043748e-889j 7.71e-50, 2.55e-160j
0.025985756081211679695 - 4.885499194651901834e-889j 1.45e-45, 4.77e-156j
0.033654649912376344971 + 1.9589281016620421615e-888j 7.04e-48, 2.33e-158j
0.041308469220311601367 - 5.0093573520394377753e-889j 1.1e-50, 3.65e-161j
0.052098929483935824303 + 3.5723387047715373266e-890j 3.29e-56, 1.09e-166j
0.043369506932564180224 + 1.1039311723239385323e-889j 3.24e-53, 1.07e-163j
0.041308469220311601367 - 1.492816412641975241e-889j 4.5e-52, 1.49e-162j
0.052360466632624036029 - 3.9988707424309301292e-890j 2.41e-57, 7.95e-168j
0.043369506932564180224 + 3.2957563514518684578e-889j 6.1e-54, 2.01e-164j
0.051048880304386164951 + 5.9108130379866766276e-890j 7.13e-57, 2.36e-167j
0.051048880304386164951 + 3.8644748996055109461e-890j 7.35e-58, 2.43e-168j
0.04517693708979002156 - 8.4587300701272300432e-890j 6e-56, 1.98e-166j
0.051662212955439377501 - 3.6577280540030134777e-890j 7.83e-58, 2.58e-168j
0.04517693708979002156 - 2.2502037458155094202e-889j 1.63e-56, 5.38e-167j
0.048116353963473970632 - 1.1794611940153747447e-889j 7.94e-58, 2.62e-168j
0.052447569178401564777 + 3.7358333649410858131e-890j 3.7e-59, 1.22e-169j
0.046752929935076393246 + 6.7291512639050708618e-890j 2.56e-58, 8.45e-169j
0.050256481507149051225 - 4.2166834553761303058e-890j 3.03e-59, 1e-169j
0.051662212955439377501 - 5.0265357900366831159e-890j 8.59e-60, 2.84e-170j
0.046752929935076393246 + 1.5977197542639857959e-889j 6.1e-59, 2.01e-169j
0.052098929483935824303 + 4.413863237529877173e-890j 5.69e-60, 1.88e-170j
0.049281047682004566844 + 4.7571688679685187817e-890j 1.92e-60, 6.35e-171j
0.048116353963473970632 - 5.5565840908964957515e-890j 2.48e-60, 8.2e-171j
0.052360466632624036029 - 3.5979566330461409155e-890j 5.58e-61, 1.85e-171j
0.049281047682004566844 + 9.0411402621665029089e-890j 7.35e-61, 2.37e-171j

Download

All rules of Legendre type can be downloaded here packed into a single file.